Article
Engineering, Electrical & Electronic
Josef Knapp, Thomas F. Eibert
Summary: Explicit formulas are presented in this article for converting spherical wave expansions with vector basis functions and scalar expansion coefficients into spherical wave expansions with scalar basis functions and vector expansion coefficients, and vice versa. These formulas are given in terms of Wigner-3-j-symbols and derived through spherical harmonics expansions. The redundancy in the expansions with vector coefficients is utilized to find compact expansions with a minimum order. The correctness of all the expansions is verified using a computer code, showing a high level of agreement between the near and far fields.
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
(2023)
Article
Physics, Multidisciplinary
O. Lisovyy, A. Naidiuk
Summary: The connection formulas between the Frobenius solutions of linear ODEs at different Fuchsian singular points can be expressed using the large order asymptotics of the corresponding power series. It is demonstrated that for various types of Heun equations, the series expansion of the relevant asymptotic amplitude can be computed systematically to any order, allowing for the verification of a recent conjecture relating to the Heun connection matrix.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Chemistry, Physical
Xiang-Yu Kong, Min Xiang, Jiancheng Fang, Dong Han, Bo Song, Lei Jiang
Summary: In the long history of traditional Chinese medicine, meridians have been considered critical channels that connect internal organs with the body surface and various parts. Despite numerous studies, the mechanism of meridians remains unclear. This paper proposes a quantum principle of meridians based on the concept of macroscopic coherence state of ion channels. Applying traditional Chinese medicine treatments on acupoints can regulate organ symptoms with the help of the quantum meridian state.
Article
Mathematics, Applied
A. Gopal, V. Rokhlin
Summary: We present an efficient scheme for constructing quadrature rules for bandlimited functions using prolate spheroidal wave functions of order zero. The scheme has an asymptotic CPU time estimate of O(n log n) to generate an n-point quadrature rule. Additionally, the CPU time cost is proportional to n for practical purposes due to the small size of the n log n term in the estimate. The algorithm's performance is demonstrated with numerical examples.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2023)
Article
Mathematics, Applied
Arpad Baricz, Pranav Kumar, Sanjeev Singh
Summary: In this paper, we investigate the geometric properties of a certain class of analytic functions obtained from the J-fraction expansion of the ratio zf'(z)/f(z). We establish that these functions map a disk domain to a starlike domain. Furthermore, we extend our study to two different normalized forms of regular Coulomb wave functions and a normalized Bessel function of the first kind using continued fractions expansions.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Chemistry, Physical
Javier Oller, Pablo Jaque
Summary: In this paper, we establish a connection between the average local ionization energy, electron affinity, and electronic Fukui functions, and derive expressions for nuclear Fukui functions beyond the highest occupied molecular orbital/lowest unoccupied molecular orbital approximation. This provides a new way to interpret and study the variation of local nucleophilicity or electrophilicity with respect to nuclear displacements, and has potential applications in molecular vibrations, internal rotations, bond dissociation, and chemical reactions.
JOURNAL OF CHEMICAL PHYSICS
(2023)
Article
Mathematics
Jihad A. Younis, Hassen Aydi, Ashish Verma
Summary: This paper introduces six new quadruple hypergeometric functions and investigates certain formulas and representations for them, such as symbolic formulas, differential formulas, and integral representations.
JOURNAL OF MATHEMATICS
(2021)
Article
Physics, Applied
B. H. McGuyer, Qi Tang
Summary: The moire effect provides an interpretation for the steering of antennas that form beams through internal spatial interferences. We use it to model six planar antennas that steer by scaling, rotating, or translating operations, demonstrating how to generate antenna designs using moire patterns.
PHYSICAL REVIEW APPLIED
(2022)
Article
Geosciences, Multidisciplinary
Zeyin Wu, Hua Huang, Yifan Wu, Xin Tao, Yuto Katoh, Xiaogang Wang
Summary: This study investigates the properties of whistler mode chorus waves using Particle-In-Cell simulations and a theoretical model. The results show that the background magnetic field nonuniformity plays a significant role in determining the amplitude and frequency chirping rate of chorus waves.
GEOPHYSICAL RESEARCH LETTERS
(2023)
Review
Biochemistry & Molecular Biology
Jen-Yang Tang, Ya-Ting Chuang, Jun-Ping Shiau, Ching-Yu Yen, Fang-Rong Chang, Yi-Hong Tsai, Ammad Ahmad Farooqi, Hsueh-Wei Chang
Summary: This review focuses on the regulating effects of natural products on miRNAs to assess the potential impacts of radiomodulation and exosome biogenesis for both the radiosensitization of cancer cells and the radioprotection of non-cancer cells.
INTERNATIONAL JOURNAL OF MOLECULAR SCIENCES
(2023)
Review
Physics, Applied
Donald C. Chang
Summary: This paper reviews a new theoretical framework to address the mystery of wave-particle duality in quantum mechanics, proposing that photons and electrons are quantized excitation waves of the vacuum represented by wave functions. It suggests that the quantum wave function truly represents a physical wave, with the wave packet appearing as a particle only in the macroscopic view.
MODERN PHYSICS LETTERS B
(2021)
Article
Mathematics, Applied
E. Weinan, Stephan Wojtowytsch
Summary: This study provides a detailed investigation of the function space of infinitely wide two-layer neural networks with ReLU activation. Different representation formulas are established. Pointwise properties of these networks are analyzed, demonstrating that certain types of functions cannot be represented by them. Furthermore, the study reveals the properties of specific functions, suggesting that two-layer neural networks may have a greater ability to approximate a variety of functions than commonly believed.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Operations Research & Management Science
Vu Thi Huong, Hong-Kun Xu
Summary: We provide exact formulas for the subdifferentials of perturbed distance functions in a normed space. Our novel method converts the problem into a parametric optimization problem and applies variational analysis technique to the optimal value function. In the convex setting, we obtain new representations for the subdifferential of perturbed distance functions that are independent of the relative position of the reference point and described directly by the input data. These results complement previous findings by Wang et al. and Li and Bounkhel, which were established using different methods.
Article
Engineering, Multidisciplinary
Hassen Aydi, Ashish Verma, Jihad Younis, Jung Rye Lee
Summary: In this paper, four new hypergeometric functions in four variables are investigated and several recursion formulas for these new functions are established. Additionally, some interesting particular cases and consequences of the results are discussed.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2022)
Article
Mathematics, Applied
Juan Luis Gonzalez-Santander
Summary: From new integral representations of the n-th derivative of Bessel functions with respect to the order, this paper derives reflection formulas for the first and second order derivatives of J(v)(t) and Y-v(t) for integral order, and for the n-th order derivatives of I-v(t) and K-v(t) for arbitrary real order. These reflection formulas are applied to extend some formulas given in the literature to negative integral order, and also lead to the calculation of an integral that has not been reported before.
RESULTS IN MATHEMATICS
(2023)
Article
Physics, Multidisciplinary
Jean-Marc Sparenberg, David Gaspard
FOUNDATIONS OF PHYSICS
(2018)
Article
Computer Science, Theory & Methods
David Gaspard, Jean-Marc Sparenberg
INTERNATIONAL JOURNAL OF QUANTUM INFORMATION
(2019)
Article
Optics
David Gaspard
Summary: This study explores the propagation of fast particles in a low-density gas at thermal equilibrium within the framework of quantum mechanics. A quantum master equation in the Redfield form, governing the reduced density matrix of the particle, is derived from first principles. The linearity of the Boltzmann equation is obtained under certain approximations. The article examines the positivity of time evolution using a Lindblad form and discusses the Born and Markov assumptions as well as other approximations related to the bath correlation function. Moreover, it demonstrates the equivalence of these master equations when the density matrix of the particle is diagonal in the momentum basis or if the collision rate is independent of the particle momentum.
Article
Optics
David Gaspard, Jean-Marc Sparenberg
Summary: This article examines the multiple scattering model of a quantum particle in a random Lorentz gas composed of fixed point scatterers. An efficient method is developed to compute the numerical map of the density of scattering resonances in the complex plane of the wave number without the need to find them individually. Two collision models are studied and some of their characteristics are revealed.
Article
Optics
David Gaspard, Jean-Marc Sparenberg
Summary: A multiple scattering model of a quantum particle interacting with a random Lorentz gas of fixed point scatterers is established, with detailed calculations of scattering amplitude, cross section, and scattering matrix properties, verifying the optical theorem and probability conservation. Numerical computations of differential and total cross sections show a distinct Airy diffraction peak for a large number of scatterers, relevant to the extinction paradox.
Article
Physics, Nuclear
David Gaspard, Jean-Marc Sparenberg, Quentin Wenda, Daniel Baye
Article
Physics, Nuclear
David Gaspard, Jean-Marc Sparenberg